(100+x)(50+x)=15000

Solution for (100+x)(50+x)=15000 equation:

Simplifying
(100 + x)(50 + x) = 15000

Multiply (100 + x) * (50 + x)
(100(50 + x) + x(50 + x)) = 15000
((50 * 100 + x * 100) + x(50 + x)) = 15000
((5000 + 100x) + x(50 + x)) = 15000
(5000 + 100x + (50 * x + x * x)) = 15000
(5000 + 100x + (50x + x2)) = 15000

Combine like terms: 100x + 50x = 150x
(5000 + 150x + x2) = 15000

Solving
5000 + 150x + x2 = 15000

Solving for variable 'x'.

Reorder the terms:
5000 + -15000 + 150x + x2 = 15000 + -15000

Combine like terms: 5000 + -15000 = -10000
-10000 + 150x + x2 = 15000 + -15000

Combine like terms: 15000 + -15000 = 0
-10000 + 150x + x2 = 0

Factor a trinomial.
(-200 + -1x)(50 + -1x) = 0

Subproblem 1
Set the factor '(-200 + -1x)' equal to zero and attempt to solve:

Simplifying
-200 + -1x = 0

Solving
-200 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '200' to each side of the equation.
-200 + 200 + -1x = 0 + 200

Combine like terms: -200 + 200 = 0
0 + -1x = 0 + 200
-1x = 0 + 200

Combine like terms: 0 + 200 = 200
-1x = 200

Divide each side by '-1'.
x = -200

Simplifying
x = -200
Subproblem 2
Set the factor '(50 + -1x)' equal to zero and attempt to solve:

Simplifying
50 + -1x = 0

Solving
50 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-50' to each side of the equation.
50 + -50 + -1x = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -1x = 0 + -50
-1x = 0 + -50

Combine like terms: 0 + -50 = -50
-1x = -50

Divide each side by '-1'.
x = 50

Simplifying
x = 50
Solution
x = {-200, 50}